Why close it just because you feel like the purpose is fulfilled or that the question had been answered?
Have you ever thought that keeping it open can allow more users to add/provide more information that is valid and valuable to the conversation and may help even further.
Also if we were allowed to close threads that we make, then we’d close it at the wrong time. The Moderators know precisely when to close or not, they are trained to be observant and have general knowledge of knowing when a thread is done its work. While we normal (non-moderator/staff) users don’t get that. And giving that power to Members (TL2) or Regulars (TL3) won’t really do much good.
There are no faults with the current system, just when you’re done with your own thread, then mute it and let a Mod close when they can. No need to flag, as they are constantly watching and keeping an eye open so, no need to bother them with flags as they will eventually, when they see fitting, close a thread after it has run its course.
I believe that your idea/thought here was well written, and a system where we have the freedom to close could’ve worked if more people knew when to close, because the main issue would be that this power could easily be misused or wrongly used and cause miscommunication and further issues so it is better as it is now with the current system/rules where the Moderators will close a thread of any kind, as that is a part of their job.